Sudden cold weather is depressing to me. I don't get aches or have physical difficulties at the onset of cold weather, but I usually feel sad, even upset when the weather turns much colder than normal.
I live in Colorado (in the USA), and it is quite common for us to see temperature changes of 30 degrees Fahrenheit (about 12 degrees Celsius) from one day to the next. Watching temperature drop 30 degrees from one day to the next just makes me feel awful, even if I know it'll happen a couple days in advance. The upset feelings don't go away until the weather warms up again.
For me, the opposite is true: if the temperature rises quickly, it gives me a feeling close to euphoria.
As far as whether this is an "ASD thing," I think it might be more common in people with ASD, with us typically less able to cope with unexpected changes when compared to the general NT population. Not sure about the body-ache aspect, though.
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DSM-5 Diagnosis: Autism Spectrum Disorder, Without accompanying intellectual or language impairment, Level 1.